Ionic compounds thermodynamic calculations

Thermodynamic modelling of solution phases lies at the core of the CALPHAD method. Only rarely do calculations involve purely stoichiometric compounds. The calculation of a complex system which may have literally 100 different stoichiometric substances usually has a phase such as the gas which is a mixture of many components, and in a complex metallic system with 10 or 11 alloying elements it is not unusual for all of the phases to involve solubility of the various elements. Solution phases will be defined here as any phase in which there is solubility of more than one component and within this chapter are broken down to four types (1) random substitutional, (2) sublattice, (3) ionic and (4) aqueous. Others types of solution phase, such as exist in polymers or complex organic systems, can also be modelled, but these four represent the major types which are currently available in CALPHAD software programmes. 

In principle, we can use the Born-Haber cycle to predict whether a particular ionic compound should be thermodynamically stable, on the basis of calculated values of U, and so proceed to explain all of the chemistry of ionic solids. The relevant quantity is actually the free energy of formation, AGf, and this is calculable if an entropy cycle is set up to complement the Born-Haber enthalpy cycle. However, in practice AHf dominates the energetics of formation of ionic compounds. 

In summary, in addition to allowing simple calculations of the energetics of ionic compounds, the Bom-Haber cycle provides insight into the energetic factors operating. Furthermore, it is an excellent example of the application of thermodynamic methods to inorganic chemistry and serves as a model for other, similar calculations not only for solids, but also for reactions in solution and in the gas phase. 

The lattice energy U of an ionic compound is defined as the energy required to convert one mole of crystalline solid into its component cations and anions in their thermodynamic standard states (non-interacting gaseous ions at standard temperature and pressure). It can be calculated using either the Born-Land6 equation... 

Preparation of consistent tabulations of thermod3maniic data is a difficult task because of the complex interrelations of the data. One new set of data can require changes in numerous related values. For inorganic thermodynamic compilations, the logical starting point is a reliable tabulation of data for the elements. If data for compounds are to be compared, they must be based on the same elemental data. Once the thermod3mamic data for the elements have been fixed, then equilibria involving the elements and compounds can be treated to fix the stabihty of the compounds. When the heats of subhmation and ionization of the elements are available, Bom-Haber cycle calculations can be carried out for ionic compounds to check the reliability of data for the compounds. 

Ethanol has also received considerable attention as a solvent over a long period of time. Data on this solvent, however, are rather few compared to methanol and very few systematic studies exist. Several solubility studies have been made since the publication of Seidell and Linke. Thomas has reported solubilities for the alkali metal iodides at 20 and 25°C, and observed a decrease in solubility with an increase in ionic radius of the cation. Deno and Berkheimer have reported the solubilities of several tetraalkylammonium perchlorates. In every case the solid phase was the pure salt. Solubilities for several rare earth compounds have been reported.Since all of these salts form solvates in the solid phase, the results cannot be used in thermodynamic calculations without the corresponding thermodynamic values for the solid phases. Solubilities of silver chloride, caesium chloride, silver benzoate, silver salicylate and caesium nitrate have been measured in ethanol, using radioactive tracer techniques. Burgaud has measured the solubility of LiCl from 10.2 to 57.6°C and observed that there is a transition from the four-solvated solid phase to the non-solvated phase at 20.4°C. 

Bom-Haber cycle An important thermodynamic calculation that is used to quantify the energy involved in making ionic compounds. 

The Born-Haber (Born, 1919 Haber, 1919) cycle shows the relationship between lattice energy and other thermodynamic quantities. It also allows the lattice energy to be calculated. The background of the Born-Haber cycle is Hess s law, which states that the enthalpy of a reaction is the same whether the reaction proceeds in one or several steps. The Born-Haber cycle for the formation of an ionic compound is shown in Figure 4.6. It is a necessary condition that... 

Although lattice energy is a useful mea.sure of an ionic compound s stability, it is not a quantity that we can measure directly. Instead, we use various thermodynamic quantities that can be measured, and calculate lattice energy using Hess s law [MI Section 5.5]. 

It should be taken into accoimt that lanthanide compoimds have a large number of excited electronic states. Although molecular constants for these states are unknown, their contribution to the thermodynamic functions can be considered by introducing a calculated correction (Gurvich et al., 1978-1984) to the electronic ground-state component. For lanthanide halides as ionic compounds, the correction can be calculated using the electronic excitation energies of the free R ions. 

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl ... 

There is another use of the Kapustinskii equation that is perhaps even more important. For many crystals, it is possible to determine a value for the lattice energy from other thermodynamic data or the Bom-Lande equation. When that is done, it is possible to solve the Kapustinskii equation for the sum of the ionic radii, ra + rc. When the radius of one ion is known, carrying out the calculations for a series of compounds that contain that ion enables the radii of the counterions to be determined. In other words, if we know the radius of Na+ from other measurements or calculations, it is possible to determine the radii of F, Cl, and Br if the lattice energies of NaF, NaCl, and NaBr are known. In fact, a radius could be determined for the N( )3 ion if the lattice energy of NaNOa were known. Using this approach, which is based on thermochemical data, to determine ionic radii yields values that are known as thermochemical radii. For a planar ion such as N03 or C032, it is a sort of average or effective radius, but it is still a very useful quantity. For many of the ions shown in Table 7.4, the radii were obtained by precisely this approach. 

In Chap. C, the thermodynamic and structural outlook of the bond, which had been the matter of discussion in Part A of this chapter, is further developed, and the model formalism, which takes advantage of the well known Friedel s model for d-transition metals but is inspired by the results of refined band calculations, is presented for metals and compounds. Also, a hint is given of the problems which are related to the nonstoichiometry of actinide oxides, such as clustering of defects. Actinide oxides present an almost purely ionic picture nevertheless, covalency is present in considerable extent, and is important for the defect structure. 

Here we consider the factors which determine whether a given compound prefers an ionic structure or a covalent one. We may imagine that for any binary compound - e.g. a halide or an oxide - either an ionic or a covalent structure can be envisaged, and these alternatives are in thermochemical competition. Bear in mind that there may be appreciable covalency in ionic substances, and that there may be some ionic contribution to the bonding in covalent substances. Since there is no simple means - short of a rigorous MO treatment - of calculating covalent bond energies, and since quantitative calculations based upon the ionic model are subject to some uncertainties, the question of whether an ionic or a covalent structure is the more favourable thermodynamically cannot be answered in absolute terms. We can, however, rationalise the situation to some extent. 

From the thermodynamic standpoint, the conclusion that AG is dominated by a very large positive AH term turns entirely on whether the calculation of the endothermicity of random, defective crystals is valid. In so far as direct thermodynamic measurements or phase equilibrium studies are available for oxide systems (and these, as the most truly ionic of allegedly nonstoichiometric compounds, should be the ones for which the Bertaut type of calculation should be least unreliable), it seems clear that the endothermicity of the random, compared with the ordered, structure has been grossly overestimated. 

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